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Proof step 89 from proof prepost-read-log (previous step)

# buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + # buf0, avol[m5] = mapped(buf0), n1 < EB_PAGE_SIZE, m5 < # avol, LEB_SIZE < n1 + # buf0 + EB_PAGE_SIZE, # buf0 < LEB_SIZE, ebm-vol-inv(avol), is-encoded(log, buf0), is-encoded(rnode(m), subarray(buf0 + mkempbuf(n1), # buf0, EB_PAGE_SIZE)), # buf0 + EB_PAGE_SIZE ≤ LEB_SIZE ⊦ n1 = 0, subarray(buf0 + mkempbuf(n1), # buf0, EB_PAGE_SIZE) = emptypage, ∃ buf, buf1. subarray(buf0, 0, # buf0 + EB_PAGE_SIZE) = buf + buf1 ∧ is-encoded(log, buf) ∧ is-encoded(rnode(m), buf1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 90:
m ≠ 0 ⊦ is-aligned(n0, m) ∧ ¬ is-aligned(n1, m) → n0 ≠ n1

Rule argument

spec: align name: is-aligned-intro seq: m ≠ 0 ⊦ is-aligned(n0, m) ∧ ¬ is-aligned(n1, m) → n0 ≠ n1 subst: [m, n1, n0] → [EB_PAGE_SIZE, n1 + # buf0, LEB_SIZE] flags: <all paths>

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ is-aligned(LEB_SIZE, EB_PAGE_SIZE); (ss)% ⊦ is-encoded(nx, buf) → is-aligned(# buf, EB_PAGE_SIZE); (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%m ≠ 0 ⊦ is-aligned(n, m) → (n < m ↔ n = 0); (s) Used terms: EB_PAGE_SIZE, n1 + # buf0, LEB_SIZE